CUMULATIVE NORMAL DISTRIBUTION TABLE
-Refer to the information above. A stock is currently selling for $42. The stock pays no dividends. An American call option on the stock has a strike price of $45 and has 6 months to
Expiration. The standard deviation of the continuously compounded rate of return of the stock
Is 25%, and the annualized risk-free rate is 3%. Use the Black-Scholes formula to calculate the
Fair value of this option.

Question

CUMULATIVE NORMAL DISTRIBUTION TABLE 
-Refer to the information above. A stock is currently selling for $42. The stock pays no dividends. An American call option on the stock has a strike price of $45 and has 6 months to
Expiration. The standard deviation of the continuously compounded rate of return of the stock
Is 25%, and the annualized risk-free rate is 3%. Use the Black-Scholes formula to calculate the
Fair value of this option.

Quizplus · Accepted Answer

Using the Black-Scholes formula, we have:
d1 = [ln(42/45) + (0.03 + (0.25^2)/2) x 0.5]/(0.25 x √0.5) = -1.08
d2 = d1 - 0.25 x √0.5 = -1.37
N(d1) = 0.1409
N(d2) = 0.0853
Therefore, the fair value of the American call option is:
C = 42 x 0.1409 - 45 x 0.0853 x e^(-0.03 x 0.5) = $2.01, which corresponds to choice B. Using the Black-Scholes formula, the fair value of the option can be calculated as follows:

d1 = [ln(42/45) + (0.03 + 0.25^2/2)*0.5]/(0.25*sqrt(0.5)) = -0.9618
d2 = d1 - 0.25*sqrt(0.5) = -1.8987
N(d1) = 0.1669
N(d2) = 0.0288

C = 42*0.1669 - 45*0.0288*exp(-0.03*0.5) = $2.01
Therefore, the fair value of the option is $2.01, which is closest to choice B.